Arcturus: Difference between revisions

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'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempers out]] the Arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic [[MOS]] ~~(2L 5s{{angbr|3/1}})~~ will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempers out]] the Arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{sl|2L 5s}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.

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| 84.8005<br />57.962

| 1768.697<br />1208.917

| style="text-align:center;" |5/3-Pythagorean is near here

| style="text-align:center;" | 5/3-Pythagorean is near here

|-

|

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== Scales ==

* [[9L 2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)

* [[9L 2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)

* [[11L 2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)

* [[11L 2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)

* [[15L 2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L 2s)

* [[15L 2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L 2s)

* [[17L 2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L 2s)

* [[17L 2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L 2s)

* [[2L 17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L 7s)

* [[2L 17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L 7s)

[[Category:Temperaments]]

[[Category:Nonoctave]]

[[Category:Tritave-equivalent temperaments]]

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 {{URWTC}}
-'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempers out]] the Arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic [[MOS]] (2L&nbsp;5s{{angbr|3/1}}) will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.
+'''Arcturus''' is the [[non-octave]] [[rank]]-2 [[regular temperament]] of the 3.5.7 [[subgroup]] that [[tempers out]] the Arcturus comma, [[15625/15309]]. Having an ~[[5/3]] as a generator, this temperament is the application of the [[Pythagorean]] principle of tuning a stack of the next higher prime number and then factoring out powers of the equivalence to [[tritave]] composition. However, a heptatonic {{sl|2L 5s}} [[MOS]] will not suffice to produce an understandable rendition of it because a very close ~5/3 generates a L:s ratio between 4:1 and 5:1, which is beginning to get too lopsided to still be a complete presentation of a temperament.
 {{tdlink|No-twos subgroup temperaments#Arcturus}}
@@ Line 632: / Line 632: @@
 | 84.8005<br />57.962
 | 1768.697<br />1208.917
-| style="text-align:center;" |5/3-Pythagorean is near here
+| style="text-align:center;" | 5/3-Pythagorean is near here
 |-
 |
@@ Line 869: / Line 869: @@
 == Scales ==
-* [[9L 2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)
+* [[9L&nbsp;2s (3/1-equivalent)]] (mini chromatic, aka sub-Arcturus)
-* [[11L 2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)
+* [[11L&nbsp;2s (3/1-equivalent)]] (anti-chromatic, aka anti-Arcturus)
-* [[15L 2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L 2s)
+* [[15L&nbsp;2s (3/1-equivalent)]] (mini enharmonic, aka super-Arcturus 15L&nbsp;2s)
-* [[17L 2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L 2s)
+* [[17L&nbsp;2s (3/1-equivalent)]] (enharmonic, aka super-Arcturus 17L&nbsp;2s)
-* [[2L 17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L 7s)
+* [[2L&nbsp;17s (3/1-equivalent)]] (anti-enharmonic, aka trans-Arcturus 2L&nbsp;7s)
 [[Category:Temperaments]]
 [[Category:Nonoctave]]
 [[Category:Tritave-equivalent temperaments]]